Problem: $\dfrac{5}{9} \div \dfrac{8}{5} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{8}{5}$ is $\dfrac{5}{8}$. Therefore: $ \dfrac{5}{9} \div \dfrac{8}{5} = \dfrac{5}{9} \times \dfrac{5}{8} $ $ \phantom{\dfrac{5}{9} \times \dfrac{5}{8}} = \dfrac{5 \times 5}{9 \times 8} $ $ \phantom{\dfrac{5}{9} \times \dfrac{5}{8}} = \dfrac{25}{72} $